Finance

The most fundamental factors that affect the cost of money or the interest rates in an economy.
The cost of money primarily is affected by four factors (i) Production opportunities which implies that the greater the cash generating ability of the asset is, the more will be investors willingness to acquire it. (ii) Time preference means how much is the willingness to let go current consumption for future, the greater is the preference for current consumption, the greater will be the interest rate or required rate of return (iii) Risk associated with returns means that the return will not be provided as expected, hence the higher the risk the higher will be interest rate or required rate of return on an investment (iv) Level of expected inflation, i.e. how much price will increase during the given period of time so, the greater the expected inflation is, the greater will be the interest rate or required rate of return. Along with these factors, general level of interest rates will also be influenced by other factors like, Federal Banks Monetary Policy, Fiscal deficit, foreign trade deficits and level of macroeconomic and business activities.

What is the real risk-free rate of interest (r) and the nominal risk-free rate (rRF)  How are these two rates measured

Real risk free rate is the rate of riskless or default free securities and is not adjusted for inflation, i.e a rate in the absence of inflation. Rate of return on US treasury bills is considered as risk free rate. It can be calculated by subtracting expected rate of inflation from the rate of return on short term T-bills. Nominal risk free rate is inflation adjusted risk free rate which is equal to real risk free rate plus inflation premium. Inflation premium is defined as average rate of inflation expected during the life of an investment.

Define the terms inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP).  Which of these premiums is included when determining the interest rate on (1) short-term U.S. Treasury securities, (2) long-term U.S. Treasury securities, (3) short-term corporate securities, and (4) long-term corporate securities  Explain how the premiums would vary over time and among the different securities listed above.

Inflation premium It is a premium which is added to the real risk free rate so as to adjust on inflation basis.

Default Risk premium It is a premium which safeguards the investor against the probability of issuers defaulting the loan, in other words, not being able to provide the expected return. It is calculated by finding the difference between US T-bills and corporate bonds of same maturity.

Liquidity Premium if an asset cannot be sold easily at an expected price, then a liquidity premium is added to the total expected rate of return.

Maturity Risk Premium It is a premium which is added to the interest rate to reflect the probability of capital loss because of increase in interest rates in longer maturity securities.
Short term US Treasury securities will have inflation premium only.
Long term treasury securities will have inflation premium and maturity risk premium
Short term corporate securities will have rates equivalent to real risk free rate plus inflation, liquidity and default risk premiums.

Long term corporate securities will have rates equivalent to real risk free rate plus inflation, liquidity, default risk and maturity risk premiums.

What is the term structure of interest rates  What is a yield curve
The relationship between yields and maturity of securities or the relationship between short term and long term interest rates is defined as the term structure of interest rates. A graphical representation of this relationship is known as yield curve.

Suppose most investors expect the inflation rate to be 5 next year, 6 the following year, and 8 thereafter.  The real risk-free rate is 3.  The maturity risk premium is zero for bonds that mature in 1 year or less, 0.1 for 2-year bonds, and then the MRP increases by 0.1 per year thereafter for 20 years, after which it is stable.  What is the interest rate on 1-, 10-, and 20-year Treasury bonds  Draw a yield curve with these data.  What factors can explain why this constructed yield curve is upward sloping
Risk free rate Rf 3
Infaltion premium IP
1 year T bond  5
10 year T bond  (5688888888)10  7.5
20 year T bond  (56888888888888888888)20  7.75
Maturity Risk Premium MP
1 year T bond  0
10 year T bond  0.1 x 9 years  0.9
20 year T bond  0.1 x 19 years  1.9
Total interest rate  Rf IPMRP
1 year T bond  3 5  0  8
10 year T bond  3  7.5  0.9  11.4
20 year T bond  3  7.75  1.9  12.65

The yield curve is affected by expected inflation rate, liquidity preference and supply and demand conditions in long term and short term markets.  The yield curve is upward sloping because IP and MRPs are increasing with the passage of time thus increasing the rate of interest.
At any given time, how would the yield curve facing a AAA-rated company compare with the yield curve for U.S. Treasury securities  At any given time, how would the yield curve facing a BB-rated company compare with the yield curve for U.S. Treasury securities  Draw a graph to illustrate your answer.

The yield curves of corporations will always lie above the yield curve for Treasury because obviously they carry more risk than T bonds. The greater the riskiness or the lower the rating, the farther and higher the yield curve of the bond will be from the yield of T bonds.

What is the pure expectations theory  What does the pure expectations theory imply about the term structure of interest rates

Pure expectations theory states that the yield curve of bond is dependent upon expected rate of inflation. This implies that investors do not take into account the maturity risk and are indifferent between short term and long term securities. Hence, if expected inflation rates keeps rising, the yield curve will upward sloping and if the rates are expected to decline, the yield will be downward sloping.

Suppose that you observe the following term structure for Treasury securities
Maturity Yield
 1 year 6.0
 2 years 6.2
 3 years 6.4
 4 years 6.5
 5 years 6.5

Assume that the pure expectations theory of the term structure is correct. (This implies that you can use the yield curve given above to back out the markets expectations about future interest rates.) What does the market expect will be the interest rate on 1-year securities 1 year from now  What does the market expect will be the interest rate on 3-year securities 2 years from now
Interest rate one year from now
(1.062)2  (1.06) x (1  x)
1.1278  1.06  1  x
1.0640 -1  x

Hence, interest rates 1 year from now on 1 year security will be 6.4
Similarly,
(1.065)  5  ((1.06)  2) x ((1  x) 3)
1.3701  1.1278  ((1  x)  3)
(1.214)  (13) - 1  x
1.067- 1  x

Therefore, interest rates 2 years from now on 3 years securities will be 6.7